Depends, see if glue is damaged by liquids came out from capacitors. See if when you move them, one or both of conection pins/wires are corroded and disconnect from capacitors' body. Then sure they are defected.
If they are in supply line check with a osciloscope their riple.
Hope to help.
Regards,
John

The glue may have become discolored merely due to age and heat, not necessarily due to exposure to electrolyte.

It would be a good idea to clean out the board of all traces of old glue as this old glue can become conductive and cause its own set of headaches.

It would also be a good idea to check the electrolytic capacitors for high ESR (equivalent series resistance) and replace the cap you're checking if its ESR is too high.

Or, you can just assume the caps are worn out from age and use and proceed to replace them all with a fresh set.

You may also need to check other parts (resistors, transistors, etc.) to be sure they are also good and measure within specs. You should also check the circuits to see if they measure up according to the service manual (if you've got one).